\begin{tikzpicture}
    \tkzDefPoints{0/0/B, 2/0/C,  1.5/2/A}
    \tkzDefPointOnLine[pos=1.5](A,B)  \tkzGetPoint{D}
    \tkzDefPointOnLine[pos=1.5](A,C)  \tkzGetPoint{E}
    \tkzDefLine[bisector,normed](D,B,C)  \tkzGetPoint{M}
    \tkzDefLine[bisector,normed](B,C,E)  \tkzGetPoint{N}
    \tkzInterLL(B,M)(C,N)  \tkzGetPoint{F}

    \tkzDrawPolygon(A,B,C)
    \tkzDrawSegments(B,D  C,E  B,M  C,N)
    \tkzDrawLine[add=0 and 1.5](B,M)
    \tkzDrawLine[add=0 and 1.7](C,N)
    \tkzLabelPoints[above](A)
    \tkzLabelPoints[left](B,D)
    \tkzLabelPoints[right](C,E,F)
\end{tikzpicture}

